Expand menu menu_open Minimize Start chapters Home History history History expand_more
{{ item.displayTitle }}
navigate_next
No history yet!
Progress & Statistics equalizer Progress expand_more
Student
navigate_next
Teacher
navigate_next
{{ filterOption.label }}
{{ item.displayTitle }}
{{ item.subject.displayTitle }}
arrow_forward
No results
{{ searchError }}
search
menu_open
{{ courseTrack.displayTitle }}
{{ statistics.percent }}% Sign in to view progress
{{ printedBook.courseTrack.name }} {{ printedBook.name }}
search Use offline Tools apps
Login account_circle menu_open

Properties of Inequalities

Rule

Properties of Inequalities

An inequality with real numbers have certain properties.

Rule

Anti Reflexive Property

A real number can never be less than or greater than itself. Therefore, a number is always equal to itself,

Rule

Anti Symmetry Property

Two real numbers, and cannot be less than and greater than each other at the same time.

If then
If then

Rule

Transitive Property

Just like the transitive property of equality, if is less than and is less than must be less than as well.

If and then

The inequality signs can be flipped and the relation will still be true.

If and then

Rule

Addition Property

The addition property applies for inequalities as well.

If then

Rule

Subtraction Property

For any given inequality it is possible to subtract a real number from both sides and the inequality will still hold true.

If then

Rule

Multiplication Property

The multiplication property for inequalities differ from the multiplication property of equality. Depending on the value of the multiplier, there are three different cases.

If
If
If